Cancellous Bone Strength Measurements with the Osteopenetrometer

Development and initial validation of a novel smoothed-particle hydrodynamics-based simulation model of trabecular bone penetration by metallic implants

A novel computational model of implant migration in trabecular bone was developed using smoothed-particle hydrodynamics (SPH), and an initial validation was performed via correlation with experimental data. Six fresh-frozen human cadaveric specimens measuring 10 × 10 × 20 mm were extracted from the proximal femurs of female donors (mean age of 82 years, range 75-90, BV/TV ratios between 17.88% and 30.49%). These specimens were then penetrated under axial loading to a depth of 10 mm with 5 mm diameter cylindrical indenters bearing either flat or sharp/conical tip designs similar to blunt and self-tapping cancellous screws, assigned in a random manner. SPH models were constructed based on microCT scans (17.33 µm) of the cadaveric specimens. Two initial specimens were used for calibration of material model parameters. The remaining four specimens were then simulated in silico using identical material model parameters. Peak forces varied between 92.0 and 365.0 N in the experiments, and 115.5-352.2 N in the SPH simulations. The concordance correlation coefficient between experimental and simulated pairs was 0.888, with a 95%CI of 0.8832-0.8926, a Pearson ρ (precision) value of 0.9396, and a bias correction factor Cb (accuracy) value of 0.945. Patterns of bone compaction were qualitatively similar; both experimental and simulated flat-tipped indenters produced dense regions of compacted material adjacent to the advancing face of the indenter, while sharp-tipped indenters deposited compacted material along their peripheries. Simulations based on SPH can produce accurate predictions of trabecular bone penetration that are useful for characterizing implant performance under high-strain loading conditions. © 2017 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 36:1114-1123, 2018.

A novel fracture mechanics model explaining the axial penetration of bone-like porous, compressible solids by various orthopaedic implant tips

Many features of orthopaedic implants have been previously examined regarding their influence on migration in trabecular bone under axial loading, with screw thread design being one of the most prominent examples. There has been comparatively little investigation, however, of the influence that implant tip design has on migration under axial loads. We present a novel fracture mechanics model that explains how differences in tip design affect the force required for axial penetration of porous, compressible solids similar to trabecular bone. Three tip designs were considered based on typical 5 mm diameter orthopaedic locking screws: flat and conical tip designs, as well as a novel elastomeric tip. Ten axial penetration trials were conducted for each tip design. In order to isolate the effect of tip design on axial migration from that of the threads, smooth steel rods were used. Tip designs were inserted into polyurethane foam commonly used to represent osteoporotic trabecular bone tissue (ASTM Type 10, 0.16 g/cc) to a depth of 10 mm at a rate of 2 mm/min, while force and position were recorded. At maximum depth, elastomeric tips were found to require the greatest force for axial migration (mean of 248.24 N, 95% Confidence Interval [CI]: 238.1-258.4 N), followed by conical tips (mean of 143.46 N, 95% CI: 142.1-144.9 N), and flat tips (mean of 113.88 N, 95% CI: 112.2-115.5 N). This experiment was repeated in cross-section while recording video of material compaction through a transparent window. Strain fields for each tip design were then generated from these videos using digital image correlation (DIC) software. A novel fracture mechanics model, combining the Griffith with porous material compaction, was developed to explain the performance differences observed between the three tip designs. This model predicted that steady-state stress would be roughly the same (~ 4 MPa) across all designs, a finding consistent with the experimental results. The model also suggested that crack formation and friction are negligible mechanisms of energy absorption during axial penetration of porous compressible solids similar to trabecular bone. Material compaction appears to be the dominant mechanism of energy absorption, regardless of tip design. The cross-sectional area of the compacted material formed during migration of the implant tip during axial penetration was shown to be a strong determinant of the force required for migration to occur (Pearson Coefficient = 0.902, p < .001). As such, implant tips designed to maximize the cross-sectional area of compacted material - such as the elastomeric and conical tips in the present study - may be useful in reducing excessive implant migration under axial loads in trabecular bone.

The effect of osteoarthritis on the regional anatomical variation of subchondral trabecular bone in the femoral head

BACKGROUND

The subchondral trabecular bone is located deep inside the articular cartilage, with the subcapital region carrying up to 70% of the diurnal loads occurring in the hip joint. This leads to severe regional anatomical variations of subchondral trabecular bone in the femoral head and the purpose of this study was to examine whether osteoarthritis affects these topographic characteristics.

METHODS

60 femoral heads were harvested during hip replacement and studied by osteopenetration at 8 pre-defined angles, at a penetration rate of 1mm/s. Twenty-eight of the donors underwent surgery due to osteoarthritis, whereas the remaining were trauma patients with hip fractures. To correlate these measurements to non-invasive data, all specimens were scanned by micro Computed Tomography (μCT) prior to experimentation. A cross-sectional area, perpendicular to the needle penetration pathway, was analyzed and the deviations compared to the recorded osteopenetration energy.

FINDINGS

The experiments revealed significant topographical deviations in the trabeculae. These were more pronounced in the osteoarthritic samples which also required overall higher osteopenetration energy. A notable dependency of the directional bone strength to its cross-sectional characteristics was observed. Although the effect of "gender" on osteopenetration energy was proven to be significant, gender was not considered an independent variable in a regression model correlating osteopenetration energy to 2D trabecular bone density as this did not improve the value of the adjusted R(2).

INTERPRETATION

The investigation provided refined insight into femoral head load-bearing capacity of patients suffering from osteoarthritis, as a comparison of osteoarthritic to healthy samples illustrated that subchondral trabecular bone in the femoral head region is subjected to increased remodeling and demineralization, reflected in higher osteopenetration values.

A New Method to Intra-Operatively Measure Local Bone Strength in Osteoporotic Bone Using a Modified Surgical Tool

The aim of this study was to test a novel method for intra-operative assessment of osteoporotic bone fracture strength using a surgical tool instrumented with a strain gauge and compare the device with cortical width (CW) measurements in the distal radius. The force needed to puncture the cortex (FNP) was quantified with the device and found to strongly correlate with bone mineral density (BMD) in the diaphysis (adj. R2 = 0.66, p < 0.001). Screw pullout studies were performed and correlation between FNP and screw pullout strength (SPS) was modest (adj. R2 = 0.34 with p < 0.05). CW correlated well with BMD (adj. R2 = 0.7, p < 0.0001) and SPS (adj. R2 = 0.5, p = 0.002) in the diaphysis. This technology may allow objective intra-operative assessment of bone strength to provide surgeons another tool for decision making on fixation strategies appropriate to the area of bone treated.

Bone properties of the humeral head and resistance to screw cutout

Surgical treatment of fractures involving the proximal humeral head is hampered by complications. Screw cutout is the major pitfall seen in connection with rigid plating. We have exploited a bony explanation for this phenomenon.

Evaluation of bone strength: correlation between measurements of bone mineral density and drilling force

Bone drilling is a major part of modern orthopaedic surgery which involves the internal fixation of fractured bones. The investigation of bone drilling described in this paper demonstrates the contribution of automation technology towards the study of bone strength. The aim of this preliminary investigation is to establish a relationship between bone drilling forces and measurements of bone mineral density (BMD) by dual energy X-ray absorptiometry (DXA). A linear relationship with a high coefficient of correlation has been found between average drilling forces and BMD measurements at both the greater trochanter and the femoral head of porcine femurs when drilling in the anterior-posterior (AP) direction (i.e. the direction of the DXA scan). It has also been found that in the normal drilling direction (i.e. in the cervical axis direction), which is orthogonal to the DXA scanning direction, there are similar trends between the drilling forces and BMD levels in regions where bone density is more consistent (e.g. the femoral head). The findings of this investigation indicate that analysis of bone drilling forces has the potential to provide useful information about the strength of bone.

Growth hormone increases vertebral and femoral bone strength in osteopenic, ovariectomized, aged rats in a dose-dependent and site-specific manner

The aim of the study was to assess the effect of growth hormone (GH) as restorative therapy in an aged, ovariectomized rat model with established osteopenia. The study was planned as a dose-response study, and four different skeletal sites were investigated by mechanical testing and measurements of bone mass and dimensions. Twelve-month-old virgin F344 rats were divided into eight groups with ten animals per group: (1) sham operated (sham); (2) ovariectomized (ovx); (3) sham + solvent vehicle (sv); (4) ovx + sv; (5) ovx + GH 50 microg/kg body weight/day; (6) ovx + GH 1.25 mg/kg body weight/day; (7) ovx + GH 2.5 mg/kg body weight/day; and (8) ovx + GH 5.0 mg/kg body weight/day. Groups 1 and 2 were killed after 3 months to establish that bone loss had occurred due to ovx. One month later, the remaining groups began 3 months of treatment, at the end of which the animals were also killed. The effects of ovariectomy (ovx) and GH therapy were measured at four skeletal sites: lumbar vertebrae; femoral diaphysis; femoral neck; and distal femoral metaphysis. Ovariectomy induced a significant loss of bone strength at all sites apart from the femoral neck. The loss was most pronounced at the distal femoral metaphysis. GH was able to reverse the ovx-induced loss of strength at the vertebral site in a dose-dependent manner. At the femoral diaphyseal site, GH not only reversed the ovx-induced changes but increased load values significantly above sham level. However, at the distal femoral metaphysis, which is dominated by cancellous bone, only partial reversal was seen after GH treatment. The lowest GH dose had no significant effect at any site tested. We conclude that GH treatment can reestablish vertebral bone loss due to ovariectomy in a dose-dependent manner. The restorative effect is only partial at the distal femoral metaphysis even at a high dose. At skeletal sites with less pronounced ovx-induced bone loss (femoral neck and diaphysis), GH treatment increased bone strength to sham level or above sham level. Therefore, the effect of ovariectomy is dependent upon the skeletal site investigated, and the effect of GH treatment is dependent on both the skeletal site and the size of the ovx-induced bone loss at this site.

Bone strength and material properties of the glenoid

The quality of the glenoid bone is important to a successful total shoulder replacement. Finite element models have been used to model the response of the glenoid bone to an implanted prosthesis. Because very little is known about the bone strength and the material properties at the glenoid, these models were all based on assumptions that the material properties of the glenoid were similar to those of the tibial plateau. The osteopenetrometer was used to assess the topographic strength distribution at the glenoid. Strength at the proximal subchondral level of the glenoid averaged 66.9 MPa. Higher peak values were measured posteriorly, superiorly, and anteriorly to the area of maximum concavity of the glenoid joint surface known as the bare area. One millimeter underneath the subchondral plate, average strength decreased by 25%, and at the 2 mm level strength decreased by 70%. The contribution of the cortical bone to the total glenoid strength was assessed by compression tests of pristine and cancellous-free glenoid specimens. Strength decreased by an average of 31% after the cancellous bone was removed. The material properties of the glenoid cancellous bone were determined by axial compression tests of bone specimens harvested from the central part of the glenoid subchondral area. The elastic modulus varied from approximately 100 MPa at the glenoid bare area to 400 MPa at the superior part of the glenoid. With the elastic constants used a predictor of the mechanical anisotropy, the average anisotropy ratio was 5.2, indicating strong anisotropy. The apparent density was an average 0.35 gr. cm-3, and the Poisson ratio averaged 0.263. According to our findings the anisotropy of the glenoid cancellous bone, details concerning the strength distribution, and the load-bearing function of the cortical shell should be considered in future finite element models of the glenoid.

Temporal expression of the anabolic action of PTH in cancellous bone of ovariectomized rats

When administered intermittently, parathyroid hormone (PTH) is a potent anabolic agent in both human and animal bone. To improve our understanding of this anabolic effect, we have examined the time course of PTH action in an established animal model of estrogen deficiency-induced bone loss: the ovariectomized rat. Animals were ovariectomized (Ovx) and allowed to lose bone for 6 weeks. A dose of 20 micrograms/kg/d of rat PTH (1-34) was administered s.c., 6 days each week for periods of 1, 2, 3, 4, 6 and 8 weeks. Animals were sacrificed for evaluation of skeletal histomorphometry of the proximal tibia and mechanical strength of the cancellous bone in the marrow cavity of the distal femur. Cancellous bone volume (Cn-BV/TV) increased gradually over 8 weeks of treatment (16.8 +/- 1.6 to 24.1 +/- 2.7%) as did the bone formation rate (0.308 +/- 0.054 to 1.659 +/- 0.293 microns3/micron2/d), as determined by an increase in both total mineralization surface (15.5 +/- 2.1 to 42.7 +/- 5.0%) and mineral apposition rate (1.88 +/- 0.20 to 3.55 +/- 0.39 microns/d). The largest increments in these variables reflecting bone formation occurred over the first week of treatment. This bone formation was accompanied by an increase in trabecular thickness (Tb.Th) (55.3 +/- 3.4 to 80.5 +/- 5.0 microns) without a corresponding increment in trabecular number (Tb.N) (3.65 +/- 0.17 to 3.55 +/- 0.26). Extensive tetracycline labels were visualized on the surface of trabecular rod-like and plate-like structures. A small transient, though not statistically significant, increase occurred in both eroded surface and urinary pyridinoline concentration immediately after the onset of PTH administration. Osteocalcin showed a small decrement in the first two weeks after PTH administration, but the levels were elevated when compared with the Ovx control in later weeks. Mechanical strength of the cancellous bone also increased significantly with PTH treatment (20.5 +/- 2.4 to 46.1 +/- 10.0 Newtons). Our results showed that: 1) intermittent PTH treatment of Ovx rats elicited an immediate increase of bone formation activity by the existing osteoblasts, 2) the increase of Cn-BV/TV after PTH administration resulted primarily from an increase in Tb.Th, and 3) improved mechanical strength after PTH treatment can be achieved by increases in Tb.Th without an increase in Tb.N.

Effects of reciprocal treatment with estrogen and estrogen plus parathyroid hormone on bone structure and strength in ovariectomized rats

Intermittent administration of PTH has been found to be an effective anabolic agent in cancellous bone. We have reported previously that combined treatment with PTH and estrogen in estrogen-deficient rats was beneficial in correcting established osteopenia. To determine if the beneficial effects of PTH therapy can be preserved by estrogen alone and whether PTH therapy can be effective in treating osteopenic subjects stabilized with estrogen, we have undertaken a "crossover" study in the rat model of estrogen-deficiency induced osteopenia. Six-month-old female rats were ovariectomized and after 5 wk treated for 8 wk with vehicle, 30 micrograms/kg per day of rPTH(1-34) plus 15 micrograms/kg per day of 17 beta-estradiol or 17 beta-estradiol alone. One group from each treatment regimen was then sacrificed and for an additional 8 weeks the remaining rats were (a) maintained on their previous treatment; (b) "crossed over" to their reciprocal treatment; or (c) administered vehicle only. At the end of this second 8-wk treatment period all rats were sacrificed. Bone mineral density of the distal femur, histomorphometric measurements of the proximal tibia and mechanical testing of the distal femur and selected vertebral bodies were performed. Our results demonstrated that (a) the gains in bone mass, trabecular connectivity and mechanical strength induced by PTH can be maintained by estrogen alone, but are reversed when both agents are withdrawn; and (b) rats with established osteopenia, maintained on estrogen treatment alone, can derive the full beneficial effects from the addition of PTH to the treatment at a later date. These data indicate that combined and/or sequential use of antiresorptive and anabolic agents may be a promising approach to the treatment of osteoporosis.

Topographical distribution of trabecular bone strength in the human os calcanei

Mechanical properties of twenty human os calcanei were determined by uniaxial compression testing of bone specimens from facies articularis talaris posterior, facies articularis cuboidea, and tuber calcanei. Specimens were taken oriented perpendicular to the planes of the facies articularis, and in tuber along the presumed loading axis throughout the gait cycle. Young's modulus and strength at facies articularis cuboidea and facies articularis talaris posterior were about three times those at the tuber calcanei. The variation of the relationship between Young's modulus and apparent density indicated differences in the orientation of the trabecula, in relation to the direction of evaluation between these locations. A more detailed analysis of the topographical variation of strength within each location was made using penetration testing of a further nineteen specimens. The results of both types of measurements indicated that the major part of the load during walking is carried by facies articularis talaris posterior and facies articularis cuboidea.

A radiological analysis of uncemented PCA tibial implants with a follow-up period of 4-7 years

A total of 63 uncemented PCA tibial implants were followed radiologically for a period of 4-7 years to establish whether primary fit, alignment, bone quality, age, and diagnosis have an effect on radiological results. Fifty-eight of the 63 tibial plateaus investigated (92%) showed excellent or good radiological results. In three cases the implant was rated radiologically endangered and in two cases radiologically loose. The results show that successful long-term anchorage depends principally on a primary stable fit. If implantation is inexact, poor bone quality, improper alignment, advanced age, and rheumatoid arthritis may be responsible for unsatisfactory radiological results. The authors conclude that particular importance must be attached to exact primary fixation when several unfavorable factors are encountered.

Cancellous bone material properties in osteoarthritic and rheumatoid total knee patients

One hundred and thirty-four cancellous bone biopsy specimens were taken from the proximal tibias and distal femurs of 55 patients undergoing total knee replacement for analysis of their area fraction and mechanical testing to determine their strength and stiffness. The purpose of the study was to measure the material properties of cancellous bone taken from arthritic patients and compare these with bone from normal subjects. The results showed a wide variation of strength (0.5-18.1 MPa, mean 5.6 MPa) and stiffness (11-504 MPa, mean 152 MPa). These values are in the same range or less than those reported for bone from normal tibias.

Strength pattern of cancellous bone at the ankle joint

The strength pattern of cancellous bone was examined in 17 ankles by a cylinder compression test and in eight distal tibial specimens by an osteopenetration test.

With the compression test, 6 mm levels were examined, five levels at the tibia and three levels at the talus. Cylinders were obtained from all levels from corresponding locations. The cylinders were tested at a constant deformation rate of 5 mm/min until failure. From the load deformation curves ultimate strength, yield strength, yield strain, ultimate strain and elastic modulus were calculated.

The penetration test involves resection of the joint surface just above the subchondral bone plate at the distal tibia. Measuring force and displacement, a 2.5 mm conical needle was pushed into the bone at 25 locations in a 5 × 5 matrix. The force-displacement curves were integrated at intervals of 2 mm. Three levels were evaluated, corresponding approximately to the first level in the compression test.

The study indicates the presence of a strong antero-lateral part and a slightly weaker postero-medial part at all levels in the tibial and talar bone. The compression test at level 1 and the penetration test at levels 1, 2, and 3 in the distal tibia revealed a high strength area crossing the central part, in contrast to the proximal levels of the tibia where the central parts were very weak. At the talus, a high strength area ran along the lateral and posterior border. There were no significant differences in the profiles of ultimate strength, yield strength, and elastic modulus.

Tricon-M uncemented total knee arthroplasty. A review of 96 knees followed for longer than 2 years

Ninety-six uncemented total knee arthroplasties done using the Tricon-M prosthesis were followed for longer than 2 years. The implant has a multilevel porous surface to facilitate biologic ingrowth and flanged polyethylene pegs for immediate fixation. Each patient was matched for age, body habitus, and diagnosis to a patient with a cemented total knee arthroplasty. There was no statistical difference between the matched pairs as related to pain, eventual range of motion, stability, or patient satisfaction; the uncemented group did as well clinically as the cemented group. Subsidence of the tibial component was noted in cases of obese patients taking systemic corticosteroids and in whom there was inadequate coverage of the cut tibial plateau surface. The mean 2-year Hospital for Special Surgery rating score was 81 in the osteoarthritis group and 83 in the rheumatoid arthritis group.

Dual-photon absorptiometry of the proximal tibia

Dual-photon absorptiometric bone-mineral assay, penetration tests, and axial compression tests of the proximal tibial epiphyses were carried out in 18 human cadaver knees. The reproducibility of bone mineral assay was within +/- 12% (95% tolerance limits). Linear regression analysis with bone-mineral content as the independent variable showed a good correlation to the ultimate force obtained from the compression tests on the medial (r = 0.81) and the lateral (r = 0.90) condyles. The correlation between bone mineral content and an average of three condylar penetration tests was somewhat weaker (medical condyle: r = 0.65, lateral condyle: r = 0.62). It is concluded that dual-photon absorptiometric bone-mineral assay may be a suitable noninvasive alternative to bone-strength measurement and thus suitable for monitoring the changes in tibial condylar bone during follow-up studies.

Mechanical strength of tibial trabecular bone evaluated by X-ray computed tomography

The prospects for the use of quantitative computed tomography (QCT) for evaluation of mechanical properties of tibial trabecular bone were investigated. Computed tomography (CT) data from the proximal tibial epi- and metaphysis of six human cadaver knees were correlated with mechanical data obtained from compression tests and penetration strength measurements. In addition CT and intraoperative penetration data were compared in 20 patients. If spatial agreement between CT and mechanical measurement sites is optimized, close correlations are found between the relative linear attenuation coefficient determined by CT and the ultimate strength (r = 0.84), the yield strength (r = 0.85), the elastic modulus (r = 0.78), the ultimate energy absorption (r = 0.83), the yield energy absorption (r = 0.81), and the penetration strength (r = 0.82). It is concluded that these correlations are sufficient to make QCT a valuable tool for non-invasive evaluation of the spatial distribution of bone properties in several clinical applications.

Fixation of experimental osteotomies of the distal femur of rabbits with biodegradable material

Osteotomies of the distal femur in 19 rabbits were operatively fixed with totally biodegradable implants. Radiographic, histological, microradiographic, and oxytetracycline-labeling studies showing healing of the osteotomy within 6 weeks. The fixation proved stable sufficiently during healing of the osteotomized bone. The osteotomies united without delay and malalignment did not occur, although no external support was used and the rabbits were allowed to walk freely after the operation. Successful use of the biodegradable fixation developed in the present study was reported recently for the treatment of fractures of the ankle.

Bone strength measurements at the proximal tibia. Penetration tests and epiphyseal compressive strength

Three penetration tests were obtained from corresponding locations at each condyle of 19 proximal tibiae. The patterns of condylar cancellous bone strength varied little between knees. The medial condyle was the strongest with an average medial to lateral strength ratio of 1.9, and in most knees the medial condyle was strongest centrally while the lateral condyle was strongest posteriorly. The penetration strength at 5 successive 2 mm levels beneath the resected subchondral surface also showed a constant pattern of variation. Bone strength decreased significantly at first except at the posterolateral site, then tended to level off. The reduction of strength was most pronounced in the centre of the condyles. The penetration tests were good predictors of the static compressive strength of the proximal tibia. Correlation coefficients of approximately 0.90 were obtained indicating statistically highly significant correlations (p less than or equal to 0.00001). The tests were carried out with equipment developed for in vivo measurements of cancellous bone strength during total knee replacement. The findings confirm the close relationship of these investigations to conventional compression tests.

Cancellous bone at the knee: a comparison of two methods of strength measurement

The relation of thin-needle axial penetration tests to axial compression tests on machined specimens was examined utilizing distal femoral and proximal tibial epiphyseal cancellous bone. The penetration strength was closely related to the yield strength (r = 0.87), the ultimate strength (r = 0.86), Young's modulus (r = 0.77), the yield energy absorption (r = 0.81), and the ultimate energy absorption (r = 0.84) derived from the compression tests. Generally, femoral specimens were stronger, stiffer, and tougher than tibial specimens. Higher peak penetration strength values were obtained from the medial than from the lateral condyles. The variation of strength within compression test specimens could be expressed in terms of penetration strength; this variation differed slightly between tibial and femoral specimens, but invariably the bone deepest to the joint surface was the weakest. Accordingly, adjustments were introduced in the regression equations connecting the penetration strength to the material properties derived from the compression tests.

Tibial plateau strength patterns in experimental modular knee replacement

Nondestructive low-strain-rate compression tests were carried out on 12 human cadaver tibiae fitted with a metal modular resurfacing component on the medial or lateral condyle. The tests were done at 20 regularly spaced points on each plateau. The reproducibility of measurement was +/- 16% (95% tolerance limits). A statistically significant correlation was demonstrated between stiffness and ultimate force values obtained from the same points (r = 0.75, P less than 0.005). On the medial plateau the compressive stiffness of the system was maximal when load was applied to the center of the prosthesis, but declined sharply toward the medial and posterior margins. On the lateral plateau maximal stiffness values were obtained more posteriorly, and the stiffness gradients toward the periphery were less marked. Details of surgical technique and specific loading situations that may cause undesirable combinations of load and point of prosthetic component contact are discussed.

Bone mineral assay: its relation to the mechanical strength of cancellous bone

Photon absorptiometric (125I) bone mineral assay and low strain-rate axial compression tests were carried out on cylindrical cancellous bone specimens from the proximal tibial epiphysis of large, skeletally mature mongrel dogs. Bone mineral assay was reproducible within ±5.0 per cent (99 per cent tolerance limits). Linear regression analysis with the bone mineral concentration as the independent variable showed a strong correlation towards the ultimate strength ( r = 0.92) and the yield strength ( r = 0.89), somewhat weaker towards the elastic modulus ( r = 0.82), the ultimate energy absorption ( r = 0.79), and the yield energy absorption ( r = 0.73), and insignificant towards the ultimate strain ( r = −0.14) and the yield strain ( r = −0.18). The power relationships between trabecular bone density and compressive strength and modulus suggested by Carter and Hayes (1977) were not statistically superior to linear relationships in the relatively narrow density range reported here. The quadratic relationship between bone mineral content and energy absorption suggested for cortical bone (Currey, 1969) could not be confirmed for trabecular bone. Linear regression analysis with the elastic modulus as the independent variable showed that the regression coefficients to predict ultimate strength and yield strength are statistically indistinguishable from those found in studies on human material. It is concluded that non-destructive techniques to measure bone density and mineralization may be suitable for clinical bone strength assay.

Trabecular bone strength patterns at the proximal tibial epiphysis

The longitudinal compressive strength of trabecular bone from the human proximal tibial epiphysis was investigated in 12 autopsy specimens using multiple penetration tests with a small diameter indentor. Strength profiles were visualized by three-dimensional computerized reconstruction as a function of location on the resection surfaces. There were large variations of the maximal values between individuals, but the patterns obtained were remarkably uniform. The medial condyle showed the highest peak value in all but one knee with a mean medial-to-lateral peak value-ratio of 1.7. At the medial condyle the high strength area was relatively large with peak values being obtained centrally and anteriorly; the lateral condyle showed a more restricted, posteriorly localized area of high strength. Beneath the menisci, bone strength gradually decreased toward the margins of the condyles; likewise, bone strength decreased to reach very low values at the intercondylar region. There was a significant reduction of bone strength with the distance from the subchondral resection surface. This reduction was most pronounced at the high strength areas.